The solution for general values of the parameters is involved, so to make a qualitative point
I only consider the limit of \(Z \rightarrow - \infty \) , where classically
the condensate of Eq. (REF ) dominates.
Instead, in perturbation theory one finds that would be Goldstone bosons have a double pole at non-zero momentum, about
\(k_c\)  [1]}. Such a double pole generates a logarithmic infrared divergence at zero temperature,
and a power law divergence at nonzero temperature.
